ADA rules state that a Service animal must be trained to do "work or tasks" that help mitigate a person's disability. THe key word is "Trained" not "help". Simply being present or doing things that are natural behaviors (such as alerting to seizures) do not count as a task. If a person has depression or other mental illnesses, the service animal can be TRAINED to lead the PWD to a quiet area, help them find the car if they are in distress, or training to have a specific response to worsening symptoms. Examples, a Service animal trained to hand money to a cashier is a Service Animal, A dog trained to sit on command is not.
While it might not happen often, a PWD may be taken to court to prive that the dog is trained to respond to the disability, which involves medical records to prove the disability, training logs of the dog, and actual demonstration of tasks.
Emotional Support Animals, do not require training, but also do not have public access rights in the manner a Service Dog does. The Federal Housing Act grants a PWD the right to ask for an accomodation in a "No pet" housing situation with supporting documentation from a medical professional or therapist. These animals are not allowed in "Public" places.
Personally I mingt not use words like "Faker" in a public education piece, as sometimes these people may really believe that the pet is doing Service Dog work - the example you were using about the person with Depression - that person may really believe that the dog is acting as a service animal; better to educate them rather than insult them. Explaining that Service Dogs are generally trained for 18 to 24 months and must be able to pass a CGC (Canine Good Citizen) and PAT (Public Access Tests) in addition to being trained. While Emotional Support Animals can take these tests, it is not a requirement for them, and even if they pass these tests it does not make an ESA a Service Dog.
The real fakers are people with no disability who want to take their little pets with them every where because they are just real jerks.